Science without empiricism is just fantasy, but empiricism without science isn’t even that. Nick Stokes has an excellent demonstration of the problem with the common practice of extrapolating from curve-fitting at his blog, Moyhu.
The upshot is
The bind with fancy curve fitting is that it really can’t be used much outside the range. And within the range, it isn’t telling you anything you didn’t already know, unless you are confident that you can make a useful deduction about the physics.
The demonstration is compelling. Have a look. And that makes two hat tips in a row to William Connolley.